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Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Lafleche, Laurent (2019), Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation, Journal of Statistical Physics, 177, p. 20–60. 10.1007/s10955-019-02356-7

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Journal of Statistical Physics
Volume
177
Publisher
Springer
Pages
20–60
Publication identifier
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Author(s)
Lafleche, Laurent
Centre de Mathématiques Laurent Schwartz [CMLS]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the Vlasov equation with singular interaction, including the Coulomb potential. To reach this objective, we also prove the propagation of velocity moments and weighted Schatten norms which implies the boundedness of the space density of particles uniformly in the Planck constant .
Subjects / Keywords
Hartree equation; Nonlinear Schrödinger equation; Vlasov equation; Coulomb interaction; Gravitational interaction; Semiclassical limit; Équation de Hartree; Équation de Schrödinger nonlinéaire; Équation de Vlasov; Intéraction Coulombienne; Intéraction gravitationnelle; Limite semi-classique